To solve this problem, let's break it down step by step.

Key Information:

• Four outer pieces:
  • Two pieces of length 30 cm
  • Two pieces of length 50 cm
• Right angle at the top:
  • The top end of the kite forms a right angle, so the two outer pieces at the top (one of length 30 cm and one of length 50 cm) form a right triangle.

The kite's frame consists of six pieces, and we're asked to find the lengths of the diagonal pieces that complete the construction. These diagonal pieces will be the hypotenuses of two right-angled triangles formed by the given lengths (30 cm and 50 cm).

Step 1: Apply the Pythagorean Theorem

For the triangle formed by the pieces of 30 cm and 50 cm, we can use the Pythagorean theorem to find the length of the diagonal piece (the hypotenuse):

$c^2 = a^2 + b^2$ Where:

• $a = 30$ cm
• $b = 50$ cm
• $c$ is the diagonal (hypotenuse) length.

Now, substitute the values:

$c^2 = 30^2 + 50^2$ $c^2 = 900 + 2500$ $c^2 = 3400$ $c = \sqrt{3400}$ $c \approx 58.31 \text{ cm}$

Step 2: Conclusion

The length of each diagonal piece is approximately 58.31 cm.

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Would you like more details on how to approach this problem, or is there any part you need further clarification on?

Here are some related questions you might find interesting:

1. How would the length of the diagonal change if the top angle wasn't a right angle?
2. What other geometric shapes could be formed using the same pieces of timber dowel?
3. How do you calculate the area of a kite when you know the lengths of its diagonals?
4. Can we use the same method to find the diagonal lengths of a rectangle?
5. How would the result change if one of the outer pieces were 40 cm instead of 30 cm?

Tip: When solving problems involving right triangles, the Pythagorean theorem is a powerful tool to quickly find unknown lengths, especially when the triangle's right angle is known.